MinT - Best Known (115, 115+87, s)-Nets in Base 3

Best Known (115, 115+87, s)-Nets in Base 3

(115, 115+87, 128)-Net over F₃ — Constructive and digital

Digital (115, 202, 128)-net over F₃, using

2 times m-reduction [i] based on digital (115, 204, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 102, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(115, 115+87, 153)-Net over F₃ — Digital

Digital (115, 202, 153)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+87, 1392)-Net in Base 3 — Upper bound on s

There is no (115, 202, 1393)-net in base 3, because

1 times m-reduction [i] would yield (115, 201, 1393)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 808267 670139 577564 609436 434957 824837 514515 461955 232857 054233 552672 949539 768792 836092 250508 680635 > 3²⁰¹ [i]